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16 votes
1 answer
395 views

Geometric interpretation of the exceptional isomorphism PSp(4,3)=PSU(4,22)

It is well-known that there is an isomorphism between PSp(4,3) (the symplectic group of dimension 4 over F3) and PSU(4,22) (the unitary group defined by 4×4 unitary matrices ...
LeechLattice's user avatar
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4 votes
1 answer
186 views

Is there a unique Baer subplane in a finite Desarguesian projective plane?

An order-m subplane of a finite projective plane of order n is called a Baer subplane if n=m2. It is known that the projective plane PG(2,q) is a Baer subplane of the Desarguesian ...
LeechLattice's user avatar
  • 9,501
6 votes
1 answer
445 views

Kantor's Singer cycle theorem

I'm trying to understand the proof of Kantor's Singer cycle theorem, which asserts that if G is a subgroup of GL(n,q) containing a Singer cycle then $\operatorname{GL}(n/s,q^s) \leq ...
Sean Eberhard's user avatar
2 votes
1 answer
183 views

Is inner product preserved only by the stabiliser in a finite reflection group?

Is the following statement true for finite reflection groups? Let G be a finite reflection group acting on Rn, let x,yRn and let z be in the orbit of y. If $\...
Violetta's user avatar
3 votes
0 answers
195 views

Vector spaces over a field of prime order with certain hyperplanes

Let V be a vector space of finite dimentional d over a field of prime order p. For what values of d and p, one can find d+1 (pairwise distinct) hyperplanes (subspaces of dimension d1) $...
Alireza Abdollahi's user avatar
14 votes
0 answers
552 views

Who conjectured that a transitive projective plane is Desarguesian?

The only known finite projective plane with a transitive automorphism group is the Desarguesian plane PG(2,q) and it seems likely that there are no others, although this is not (quite) proved. ...
Gordon Royle's user avatar
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